In this story I'm reading, there are these two blokes 'aving a bit of a barney:
"Atque ea rixa adeo inter eos exarsit, ut etiam pugnis certarent. Tandem in ius ambulant."
And now a quarrel erupted between them, and they even fought with their fists. Finally they walked in ius.
I'm assuming it means something like went to court (over the matter), but I can't find that meaning of ius anywhere. Advice would be appreciated.

Trials in Rome took place before a praetor and ius is the place where that magistrate administered law. So, in ius ire, means that they went to the praetor in order to have their quarrel settled by law.
Roman trials had two parts: in iure and apud iudicem. The first part took part before the praetor (hence its name), the second one before a private judge.
This meaning of ius is widely attested in the writings of the jurists or even in Cicero's works. It was in fact the working base of the Roman legal system.